System and method for providing first arrival path (FAP) and delay spread estimation (DSE) in wireless communication system

ABSTRACT

A method for minimizing a time domain mean square error (MSE) of channel estimation (CE) includes estimating, by a processor, a power delay profile (PDP) from a time domain observation of reference signal (RS) channels; estimating, by the processor, a noise variance of the RS channels; and determining, by the processor, a first arrival path (FAP) value and a delay spread estimation (DSE) value based on the estimated PDP and the estimated noise variance for minimizing the MSE of CE.

CROSS-REFERENCE TO RELATED APPLICATION(S)

The present application claims priority to and the benefit of U.S.Provisional Patent Application Ser. No. 62/888,827, filed Aug. 19, 2019and entitled “SYSTEM AND METHOD FOR PROVIDING FIRST ARRIVAL PATH (FAP)AND DELAY SPREAD ESTIMATION (DSE) IN WIRELESS COMMUNICATION SYSTEM,” theentire content of which is hereby expressly incorporated by reference.

FIELD

The present disclosure generally relates to a wireless communicationsystem. In particular, the present disclosure relates to a system and amethod for providing first arrival path (FAP) and delay spreadestimation (DSE) in a wireless communication system.

BACKGROUND

In 5^(th) generation (5G) new radio (NR) radio access technology (RAT),if the reference signal (RS) observation is limited to a narrow band(e.g., a physical downlink shared channel (PDSCH) demodulation referencesignal (DMRS)), a frequency domain (FD) minimum mean square error (MMSE)filter is used for de-noising in channel estimation (CE). This may bereferred to as FD-MMSE CE or narrow band CE. In order to obtain theweight matrix of FD-MMSE, the frequency correlation between RS channelsand data resource element (RE) channels, as well as the frequency autocorrelation of RS channels need to be calculated. Theoretically, thefrequency correlation is calculated as the discrete Fourier transform(DFT) of power delay profile (PDP). Due to hardware complexity, thefrequency correlation function may be calculated based on uniform PDPwith length equal to the delay spread value provided by delay spreadestimation (DSE) block. Therefore, the delay spread estimation (DSE) maybe utilized for channel estimation (CE).

The above information in the Background section is only for enhancementof understanding of the background of the technology and therefore itshould not be construed as admission of existence or relevancy of theprior art.

SUMMARY

This summary is provided to introduce a selection of features andconcepts of embodiments of the present disclosure that are furtherdescribed below in the detailed description. This summary is notintended to identify key or essential features of the claimed subjectmatter, nor is it intended to be used in limiting the scope of theclaimed subject matter. One or more of the described features may becombined with one or more other described features to provide a workabledevice.

Aspects of example embodiments of the present disclosure relate to asystem and method for providing first arrival path (FAP) and delayspread estimation (DSE) in wireless communication system. According toan embodiments of the present disclosure, a method for minimizing a timedomain mean square error (MSE) of channel estimation (CE) includesestimating, by a processor, a power delay profile (PDP) from a timedomain observation of reference signal (RS) channels; estimating, by theprocessor, a noise variance of the RS channels; and determining, by theprocessor, a first arrival path (FAP) value and a delay spreadestimation (DSE) value based on the estimated PDP and the estimatednoise variance for minimizing the MSE of CE.

In one embodiment of the present disclosure, the time domain MSE is:

$\begin{matrix}{{MSE} = {1 + \frac{L\sigma^{2}}{( {1 + {L\sigma^{2}}} )^{2}} + {\lbrack {\frac{1}{( {1 + {L\sigma^{2}}} )^{2}} - \frac{2}{1 + {L\sigma^{2}}}} \rbrack{\underset{i = F}{\sum\limits^{L + F - 1}}P_{i}}}}} & (1)\end{matrix}$

-   -   wherein F and L are integers, where:

${1 \leq L \leq \frac{3N}{4}},{{- \frac{N}{4}} \leq F \leq {\frac{N}{4}.}}$wherein, σ² is the noise variance, P_(i) is power of the i-th channeltap or the uniform PDP, F is first arrival path (FAP) index, N is alength of the estimated PDP, and L is a length of the uniform PDP.

In one embodiment of the present disclosure, determining the FAP valueand the DSE value to minimize the time domain MSE includes determining,by the processor, a value of F and a value of L, wherein a minimum valueof the time domain MSE is determined based on the value of F and thevalue of L.

In one embodiment of the present disclosure, the value of L is the delayspread value for minimizing the MSE and the estimated noise variance iscapped at a signal to noise ratio (SNR)=20 dB. In one embodiment of thepresent disclosure, the determining the value of F and the value of Lfor minimizing the time domain MSE includes assigning, by the processor,a value “0” to the FAP index F; determining, by the processor, aminimized value of MSE and corresponding value of L for each F of aplurality of F values within

${{- \frac{N}{4}} \leq F < {0\mspace{14mu}{and}\mspace{14mu} 0} < F \leq \frac{N}{4}};$and determining, by the processor, the value of F and the value of Lbased on comparing minimized values of MSE for the plurality of F valueswithin

${- \frac{N}{4}} \leq F < {0\mspace{14mu}{and}\mspace{14mu} 0} < F \leq {\frac{N}{4}.}$

In one embodiment of the present disclosure, the value of F and thevalue of L correspond to a minimum value of MSE from among the minimizedvalues of MSE for the plurality of F values within

${{- \frac{N}{4}} \leq F < {0\mspace{14mu}{and}\mspace{14mu} 0} < F \leq \frac{N}{4}},$wherein the minimized values of MSE and the corresponding values of Lare determined using equation (1). In one embodiment of the presentdisclosure, the method further includes stopping a search of the valueof F and the value of L for F>0 or F<0, by the processor, in response tothe minimized value of MSE, for F within

${{- \frac{N}{4}} \leq F < {0\mspace{14mu}{or}\mspace{14mu} 0} < F \leq \frac{N}{4}},$being increased as |F| increased for n consecutive times, wherein the nis 5.

In one embodiment of the present disclosure, the method further includesscaling, by the processor, the value of F and the value of L based on adifference of sampling time between the RS channels and data resourceelements (REs) to determine a scaled value of F and a scaled value of L.In one embodiment of the present disclosure, the scaled value of F isF′, wherein F′=scaling factor×F, and the scaled value of L is L′,wherein L′=scaling factor×L, wherein

${{{scaling}\mspace{14mu}{factor}} = {\frac{\begin{matrix}{{{Sample}\mspace{14mu}{duration}}\mspace{14mu}} \\{{of}\mspace{14mu}{RSPDP}}\end{matrix}}{\begin{matrix}{{{Sample}\mspace{14mu}{duration}}\mspace{14mu}} \\{{of}\mspace{14mu}{data}\mspace{14mu}{REs}}\end{matrix}} = \frac{N_{IFFT} \times \Delta f}{N_{PDP} \times \Delta f \times \frac{12}{\rho}}}},$wherein N_(IFFT) is a size of Fast Fourier Transform (FFT), N_(PDP) is alength of the estimated PDP, Δf is a subcarrier spacing, and ρ is adensity of RS REs.

In one embodiment of the present disclosure, the method further includesdetermining, by the processor, CE and a frequency correlation betweenthe RS channels and the data REs, based on F′ and L′.

In one embodiment of the present disclosure, a system for minimizing atime domain mean square error (MSE) of channel estimation (CE) includesa memory and a processor in communication with the memory, wherein theprocessor is configured to: estimate a power delay profile (PDP) fromtime domain observation of reference signal (RS) channels; estimate anoise variance of the RS channels; and determine a first arrival path(FAP) value and a delay spread estimation (DSE) value based on theestimated PDP and the estimated noise variance for minimizing the MSE ofCE.

In one embodiment of the present disclosure, the time domain MSE is:

$\begin{matrix}{{MSE} = {1 + \frac{L\sigma^{2}}{( {1 + {L\sigma^{2}}} )^{2}} + {\lbrack {\frac{1}{( {1 + {L\sigma^{2}}} )^{2}} - \frac{2}{1 + {L\sigma^{2}}}} \rbrack{\underset{i = F}{\sum\limits^{L + F - 1}}P_{i}}}}} & (1)\end{matrix}$

wherein F and L are integers, where:

${1 \leq L \leq \frac{3N}{4}},{{- \frac{N}{4}} \leq F \leq {\frac{N}{4}.}}$

wherein, σ² is the noise variance, P_(i) is power of the i-th channeltap or the uniform PDP, F is first arrival path (FAP) index, N is alength of the estimated PDP, and L is a length of the uniform PDP.

In one embodiment of the present disclosure, the processor is furtherconfigured to: determine the FAP value and the DSE value to minimize thetime domain MSE based on determining a value of F and a value of L,wherein the processor is further configured to determine a minimum valueof the time domain MSE based on the value of F and the value of L. Inone embodiment of the present disclosure, the value of L is the delayspread value for minimizing the MSE and the estimated noise variance iscapped at a signal to noise ratio (SNR)=20 dB. In one embodiment of thepresent disclosure, the processor is further configured to: assign avalue “0” to the FAP index F; determine a minimized value of MSE andcorresponding value of L for each F of a plurality of F values within

${{- \frac{N}{4}} \leq F < {0\mspace{14mu}{and}\mspace{14mu} 0} < F \leq \frac{N}{4}};$and determine the value of F and the value of L based on comparingminimized values of MSE for the plurality of F values within

${- \frac{N}{4}} \leq F < {0\mspace{14mu}{and}\mspace{14mu} 0} < F \leq {\frac{N}{4}.}$

In one embodiment of the present disclosure, the value of F and thevalue of L correspond to a minimum value of MSE from among the minimizedvalues of MSE for the plurality of F values within

${{- \frac{N}{4}} \leq F < {0\mspace{14mu}{and}\mspace{14mu} 0} < F \leq \frac{N}{4}},$wherein the minimized values of MSE and the corresponding values of Lare determined using equation (1). In one embodiment of the presentdisclosure, the processor is further configured to stop a search of thevalue of F and the value of L for F>0 or F<0, by the processor, inresponse to the minimized value of MSE, for F within

${{- \frac{N}{4}} \leq F < {0\mspace{14mu}{and}\mspace{14mu} 0} < F \leq \frac{N}{4}},$being increased as increased for n consecutive times, wherein the n is5.

In one embodiment of the present disclosure, the processor is furtherconfigured to scale the value of F and the value of L based on adifference of sampling time between RS channels and data resourceelements (REs) to determine a scaled value of F and a scaled value of L.In one embodiment of the present disclosure, the scaled value of F isF′, wherein F′=scaling factor×F, and the scaled value of L is L′,wherein L′=scaling factor×L, wherein

${{{scaling}\mspace{14mu}{factor}} = {\frac{{Sample}\mspace{14mu}{duration}\mspace{14mu}{RS}\mspace{14mu}{PDP}}{{Sample}\mspace{14mu}{duration}\mspace{14mu}{of}\mspace{14mu}{data}\mspace{14mu}{REs}} = \frac{N_{IFFT} \times \Delta\; f}{N_{PDP} \times \Delta\; f \times \frac{12}{\rho}}}},$wherein N_(IFFT) is a size of Fast Fourier Transform (FFT), N_(PDP) is alength of the estimated PDP, Δf is a subcarrier spacing, and ρ is adensity of RS REs.

In one embodiment of the present disclosure, the processor is furtherconfigured to determine CE and a frequency correlation between RSchannels and data REs, based on F′ and L′.

BRIEF DESCRIPTION OF THE DRAWINGS

These and other features of some example embodiments of the presentdisclosure will be appreciated and understood with reference to thespecification, claims, and appended drawings, wherein:

FIGS. 1A-1C illustrate uniform PDP of a fixed length, according to oneexample embodiment of the present disclosure;

FIGS. 2A-2B illustrate examples of different sample time conversionschemes, according to one example embodiment of the present disclosure;

FIG. 3 illustrates a block diagram representation of an example system,according to one example embodiment of the present disclosure;

FIG. 4 illustrates another block diagram representation of an examplesystem for DSE, according to one example embodiment of the presentdisclosure;

FIGS. 5A-5B illustrate a flow chart illustrating an example method forDSE, according to one example embodiment of the present disclosure;

FIG. 6 illustrates the block error rate (BLER) performance in low SNRregime, according to one example embodiment of the present disclosure;and

FIG. 7 illustrates the BLER performance in high SNR regime, according toone example embodiment of the present disclosure.

DETAILED DESCRIPTION

The detailed description set forth below in connection with the appendeddrawings is intended as a description of some example embodiments of asystem and method for providing first arrival path (FAP) and delayspread estimation (DSE) in wireless communication system provided inaccordance with the present disclosure and is not intended to representthe only forms in which the present disclosure may be constructed orutilized. The description sets forth the features of the presentdisclosure in connection with the illustrated embodiments. It is to beunderstood, however, that the same or equivalent functions andstructures may be accomplished by different embodiments that are alsointended to be encompassed within the scope of the disclosure. Asdenoted elsewhere herein, like element numbers are intended to indicatelike elements or features.

In 5^(th) generation (5G) new radio (NR), if the reference signal (RS)observation is limited to a narrow band (e.g., a physical downlinkshared channel (PDSCH) demodulation reference signal (DMRS)), afrequency domain MMSE filter is used for de-noising in channelestimation (CE), which may be referred to FD-MMSE CE or narrow band CE.In order to obtain the weight matrix of FD-MMSE, the frequencycorrelation between RS channels and data resource element (RE) channels,as well as the frequency auto correlation of RS channels may becalculated. Frequency correlation may be determined as the discreteFourier transform (DFT) of PDP. Due to hardware complexity, thefrequency correlation function may be calculated based on a uniform PDPdefined by the first arrival path (FAP) and the delay spread valueprovided by the DSE block. Therefore, the FAP and the delay spreadestimation may be utilized for channel estimation (CE).

The present disclosure provides an example estimation method to measurethe FAP and the delay spread (e.g., “the example method,” or “theexample method for delay spread estimation (DSE) and measuring FAP,” or“the example method and system for DSE and measuring FAP,” or “theexample method and system for DSE”), using the estimated PDP and noisevariance (e.g., an estimated noise variance).

In some cases, a typical method may be based on path searching withgiven FAP and last arrival path (LAP) threshold. However, the estimatedLAP index in such a method may suffer from the high fluctuation of thePDP in low SNR regime, which may impact the CE performance (e.g., maynot optimize the CE performance). The present system and method providesthe FAP and an optimized delay spread value (e.g., based on theestimated PDP and the estimated noise variance) that may lower (e.g.,minimize) the mean square error (MSE) of channel estimation (CE) inresponse to a uniform PDP being used for frequency domain-minimum meansquare error (FD-MMSE) CE. For example, the FAP and delay spread valuemay be optimized such that the MSE between the estimated channels andthe ideal channels may be lowered or minimized in time domain. In somecases, different embodiments of the example method and system for DSEmay perform better than some alternative methods (e.g., path searchingbased DSE methods), for example, in low SNR regime.

In the embodiments of the example method and system for DSE of thepresent disclosure, PDP calculated by the channel state informationreference signal (CSI-RS) for tracking (TRS) may be used to acquiredelay spread estimation of the present disclosure. In embodiments of theexample method and system for DSE of the present disclosure, the PDPestimated using a synchronization signal (SS) block (physical broadcastchannel (PBCH) DMRS/SSS) and a physical downlink shared channel (PDSCH)DMRS may also be used for DSE when the TRS is absent.

Embodiments of the example method and system for DSE of the presentdisclosure may enable estimating the delay spread based on PDP and noisevariance estimated from the wideband reference signal, such as TRS, PBCHDMRS as mentioned before. In embodiments of the example method andsystem for DSE of the present disclosure, since the frequencycorrelation function is the fast Fourier transform (FFT) of PDP, theFD-MMSE weight matrix may be interpreted in time domain. The delayspread value may be optimized subsequently, to lower (or minimize) themean square error (MSE) between the estimated channels and the idealchannels, in time domain. In one embodiment, the optimality of the delayspread may be achieved, for example, by assuming infinite taps infrequency domain to implement FD MMSE CE (e.g., in practice only 6 tapsare used). Even with such an assumption, the embodiments of the examplemethod and system for DSE of the present disclosure may performrelatively close to the ideal case (e.g., calculating frequencycorrelation with ideal PDP), and therefore, may improve low SNRperformance compared to the alternative methods. In addition, the timedomain operation of the embodiments of the example method and system forDSE of the present disclosure may reduce the complexity compared to adirect optimization in frequency domain.

A system model for the implementation of the embodiments of the examplemethod and system for DSE of the present disclosure to estimate thedelay spread based on the PDP and the noise variance estimated from thewideband reference signal, such as TRS, PBCH DMRS, as mentioned before,is described in the following paragraphs.

In frequency domain, if it is assumed that p_(f) is the vector of thechannels for RS REs, and y is the observation of these RS channels, ymay be represented as:y=h _(p) +z,  (1)

In equation (1), z is the vector of the background noise, which isassumed to be independent to the RS channels, h_(p)=[h_(p1), h_(p2), . .. , h_(pN)]^(T) and of zero-mean and covariance σ²I. If it is assumedthat h is the vector of the channels for all REs within the same symbolthat are to be estimated, then, the linear minimum mean square error(LMMSE) solution for the estimate of h=[h₁, h₂, . . . , h_(M)]^(T) maybe represented as:ĥ=R _(dp)(R _(pp)+σ² I)⁻¹ y,  (2)

In equation (2), R_(dp) is the frequency correlation matrix between hand h_(p), and R_(pp) is the frequency auto-correlation matrix of h_(p);I is the identity matrix of size equal to the length of h_(p).

In some cases, frequency correlation may depend only on the frequencydomain distances. Also, in some cases, the correlation between channelsh_(i) and h_(pk) may satisfy the following relationship:R _(dp) ^([i,k]) =E[h _(i) h _(pk)*]=r _(f)(i−k),  (3)

Given the estimated PDP of channel, the frequency correlation functionr_(f)(⋅) may be represented as:

$\begin{matrix}{{{r_{f}(k)} = {\sum\limits_{i = 0}^{N - 1}{P_{i}e^{{- j}2{\pi k\Delta}\; f\;\tau_{i}}}}},} & (4)\end{matrix}$

In equation (4), N may be the length of the PDP, P_(i) and x_(i) may bethe power and delay of the i-th channel tap, respectively, k may be thefrequency distance of two channels, and Δf may be the subcarrierspacing.

In some cases, directly calculating the frequency correlation with realPDP may be challenging due to hardware complexity. However, thefrequency correlation may be simplified by assuming a uniform PDP withlength N and non-zero entries from index F to F+L−1, i.e., a PDP withnon-zero entries {P_(i)′}, ∀i∈{F, F+1, . . . , F+L−1} where:

$\begin{matrix}{P_{i}^{\prime} = \{ \begin{matrix}{{1/L},} & {F \leq i \leq {F + L - 1}} \\{0,} & {otherwise}\end{matrix} } & (5)\end{matrix}$

In equation (5), F and L are integers

${F \in \{ {{- \frac{N}{4}},\ldots\mspace{11mu},\ \frac{N}{4}} \}},{L \in {\{ {1,\ldots\mspace{11mu},\frac{3N}{4}} \}.}}$In equation (5), the total length of the uniform PDP may be N (N may notbe related to delay spread), however only L (e.g., delay spread) tapsmay be non-zero. Also, in equation (5), F may be the FAP index. Inexample embodiments of the present disclosure, a uniform PDP may bedefined by the FAP and the delay spread value.

In some cases, based on the above mentioned assumptions, the frequencycorrelation function {circumflex over (f)}_(f)(⋅) may satisfy thefollowing condition:

$\begin{matrix}{{{\hat{r}}_{f}( {k,L,F} )} = {{\sum\limits_{i = F}^{F + L - 1}{P_{i}^{\prime}e^{{- j}\; 2\;\pi\; k\;\Delta\; f\;\tau_{i}}}} = {\sum\limits_{i = F}^{F + L - 1}{\frac{1}{L}e^{{- j}\; 2\;\pi\;{{ki}/N_{fft}}}}}}} & (6)\end{matrix}$

Therefore, the correlation matrix and the auto-correlation matrixcalculated by (6) may be {circumflex over (R)}_(dp) and {circumflex over(R)}_(pp), and the estimated channel based on the uniform PDP may berepresented as:ĥ′=R _(dp)({circumflex over (R)} _(pp)+σ² I)⁻¹ y  (7)

By utilizing the embodiments of the example method and system for DSE ofthe present disclosure, given any PDP, the optimal uniform PDP mayreduce or minimize the MSE between the estimated channel (6) and theideal channel, which may be represented as:

$\begin{matrix}{\underset{F,L}{argmin}E\{ {( {\hat{h^{\prime}} - h} )^{H}( {\hat{h^{\prime}} - h} )} \}} & (8)\end{matrix}$With the above approximation, the optimization problem in (8) may berepresented as the following optimization problem:

$\begin{matrix}{{{\underset{F,L}{argmin}1} + \frac{L\sigma^{2}}{( {1 + {L\sigma^{2}}} )^{2}} + {\lbrack {\frac{1}{( {1 + {L\sigma^{2}}} )^{2}} - \frac{2}{1 + {L\sigma^{2}}}} \rbrack{\sum\limits_{i = F}^{L + F - 1}P_{i}}}}{{{s.t.1} \leq L \leq \frac{3N}{4}},{{- \frac{N}{4}} \leq F \leq {\frac{N}{4}.}}}} & (9)\end{matrix}$

In equation (9), it may be assumed that uniform PDP is circularsymmetric, so for a negative F, P_(F)=P_(F+N). In equation (9), “N” maybe the length of the PDP (e.g., not uniform PDP) used in CE and also theinput of the example method and system for DSE of the presentdisclosure. N is a fixed number and may not be changed in theembodiments of the example method and system for DSE of the presentdisclosure. In the embodiments of the example method and system for DSEof the present disclosure, a uniform PDP with L non-zero value taps maybe used to mimic the real PDP with length N. Because N>>L, the uniformPDP may have length N in order to be used in CE. In one the embodimentof the example method and system for DSE of the present disclosure,zero-value taps may be added.

For example, FIGS. 1A-1C illustrate the uniform PDP for F=0, F>0, andF<0 and different ranges of N. For example, in FIG. 1A, the value of thefirst uniform PDP 102 for non-zero taps is 1/L (as discussed withrespect to equation (5)). In FIG. 1A, tap 0˜L are non-zero taps and tapL+1˜N are zero taps. The length of the first uniform PDP 102 is L. Forexample, in FIG. 1B, the value of the second uniform PDP 104 fornon-zero taps is 1/L (as discussed with respect to equation (5)). InFIG. 1B, tap F˜L+F−1 are non-zero taps and tap 0˜F and tap L+F−1˜N arezero taps. The length of the second uniform PDP 104 is L. For example,in FIG. 1C, the value of the third uniform PDP 106 for non-zero taps is1/L (as discussed with respect to equation (5)). In FIG. 1C, tap F˜L+F−1(F<0) are non-zero taps and tap L+F−1˜N are zero taps. The length of thethird uniform PDP 106 is L. The fourth uniform PDP 108 may be anequivalent representation of the third uniform PDP 106.

In terms of hardware implementation, the complexity of calculating ametric of equation (9) may be further simplified as follows (e.g., toreduce the complexity involved in performing division in hardware orprocessor):

$\begin{matrix}{{{{{\arg\min}_{F,L}1} + \frac{L\sigma^{2}}{( {1 + {L\sigma^{2}}} )^{2}} + {\lbrack {\frac{1}{( {1 + {L\sigma^{2}}} )^{2}} - \frac{2}{1 + {L\sigma^{2}}}} \rbrack{\sum\limits_{i = F}^{L + F - 1}P_{i}}}} = {{{\arg\min}_{L}\alpha} + \lbrack {{\alpha L\sigma^{2}} - {( {2 - \alpha} ){\sum\limits_{i = F}^{L + F - 1}P_{i}}}} \rbrack}},\mspace{79mu}{\alpha = \frac{P_{sum}}{P_{sum} + {L\sigma^{2}}}}} & (10) \\{\mspace{85mu}{{{{\sim{argmin}_{L}}{\sum\limits_{i = F}^{L + F - 1}P_{i}}} + {L\sigma^{2}} - {2{\sum\limits_{i = F}^{L + F - 1}P_{i}}}} = {{L\sigma^{2}} - {\sum\limits_{i = F}^{L + F - 1}P_{i}}}}} & ( {9A} )\end{matrix}$

As evident from above, equation (9A) is simplified by assuming α=1,which may imply that hardware or processor may not need to calculate αas well as multiplication of a and other parameters in equation (10). Assuch, in equation 9A, a division operation (as shown in equation (10))may be removed, and therefore, the number of multiplication operation inhardware or processor may be reduced. In one embodiment, equation (10)may be computed by a processor.

In one embodiment, the example method and system for DSE may supportdifferent RS, and therefore, TRS may be used for embodiments of theexample method and system for DSE of the present disclosure.

The following paragraphs discuss in details the derivation of equation(9). For example, in some cases, in the frequency domain, the weightmatrix of MMSE channel may be estimated as follows:

$\begin{matrix}{{R_{dp}( {R_{pp} + {\sigma^{2}I}} )}^{- 1} = {{F_{h}{{PF}^{H}( {{FPF}^{H} + {\sigma^{2}I}} )}^{- 1}} = {{F_{h}{PF}^{H}{F( {P + {\sigma^{2}I}} )}^{- 1}F^{H}} = {F_{h}{P( {P + {\sigma^{2}I}} )}^{- 1}F^{H}}}}} & (11)\end{matrix}$

In equation (11), P=diag(P₀, P₁, . . . , P_(N-1)) is a N×N diagonalmatrix, F is a N×N matrix with (i, j)th entry

${(F)_{i,j} = {\exp( {- \frac{{j2\pi p}_{i}( {j - 1} )}{N}} )}},$F_(h) is a M×N matrix with (i,j)th entry

$( F_{h} )_{i,j} = {{\exp( {- \frac{{j2\pi h}_{i}( {j - 1} )}{N}} )}.}$

In the above channel weight matrix (e.g., equation (11)), all the N tapsin frequency domain may be used to calculate the frequency correlationwhile in practice only approximately 6 taps are used. Therefore, basedon this assumption, in time domain the MMSE weights can be presented asP_(i)/(P_(i)+σ²), i∈{0, 1, . . . , N−1}. Consequently, the time domainweights for the uniform PDP introduced in equation (5) may berepresented as:

$\begin{matrix}{U_{i}^{\prime} = \{ \begin{matrix}{{\frac{1}{L}\text{/}( {\frac{1}{L} + \sigma^{2}} )},} & {F \leq i \leq {F + L - 1}} \\{\mspace{121mu}{0,}} & {{otherwise}\mspace{85mu}}\end{matrix} } & (12)\end{matrix}$

Based on the above, the time domain observation of the RS channels maybe {h_(p0) ^((t)), h_(p1) ^((t)), . . . , h_(pN-1) ^((t))}. In oneembodiment, y_(i) ^(t) may be the observation at tap i and in such acase, y_(i) ^(t) may be represented as:y _(i) ^((t)) =h _(pi) ^((t)) +z _(i) ^((t))  (13)

In equation (13), z_(i) ^(t) is the background noise in time domain,which may be independent to the RS channels and of zero-mean andvariance σ².

The optimal uniform PDP to lower or minimize the following mean squareerror of channel estimation may be:

$\begin{matrix}{{( {L_{o},F_{o}} ) = {\underset{F,L}{argmin}\mspace{14mu} E\{ {\sum\limits_{i = 0}^{N - 1}\;{( {{U_{i}^{\prime}y_{i}^{t}} - h_{pi}^{(t)}} )^{*}( {{U_{i}^{\prime}y_{i}^{t}} - h_{pi}^{(t)}} )}} \}}}{{{s.t.1} \leq L \leq \frac{3N}{4}},{{- \frac{N}{4}} \leq F \leq {\frac{N}{4}.}}}} & (14)\end{matrix}$

It may be observed that the difference between (8) and (14) is that (14)is for time domain channel. Therefore, based on the above, MSE may berepresented as:

$\begin{matrix}{{MSE} = {E\{ {\sum\limits_{i = 0}^{N - 1}\;{( {{U_{i}^{\prime}( {h_{pi}^{(t)} + z_{i}^{(t)}} )} - h_{pi}^{(t)}} )^{*}( {{U_{i}^{\prime}( {h_{pi}^{(t)} + z_{i}^{(t)}} )} - h_{pi}^{(t)}} )}} \}}} & (15) \\{= {\sum\limits_{i = 0}^{N - 1}\;\{ {{U_{i}^{\prime}P_{i}U_{i}^{\prime}} + P_{i} + {U_{i}^{\prime}\sigma^{2}U_{i}^{\prime}} - {2U_{i}^{\prime}P_{i}}} \}}} & (16) \\{= {{\sum\limits_{i = 0}^{N - 1}\; P_{i}} + {\sum\limits_{i = F}^{L + F - 1}\;{( \frac{\frac{1}{L}}{\frac{1}{L} + \sigma^{2}} )^{2}\sigma^{2}}} + {\sum\limits_{i = F}^{L + F - 1}\;\{ {\lbrack {( U_{i}^{\prime} )^{2} - {2U_{i}^{\prime}}} \rbrack P_{i}} \}}}} & (17) \\{= {1 + \frac{L\;\sigma^{2}}{( {1 + {L\;\sigma^{2}}} )^{2}} + {\lbrack {\frac{1}{( {1 + {L\;\sigma^{2}}} )^{2}} - \frac{2}{1 + {L\;\sigma^{2}}}} \rbrack{\sum\limits_{i = F}^{L + F - 1}\; P_{i}}}}} & (18)\end{matrix}$

With respect to (16), P_(i)=E(h_(pi) ^((t)*)h_(pi) ^((t))) may be usedto denote the PDP for RS REs channel. Also, E(z_(i) ^((t))*h_(pi)^((t)))=E(h_(pi) ^((t)*)z_(i) ^((t)))=0, because noise may beindependent with channels.

With respect to (18), due to the uniform power is constraint Σ_(i=0)^(N-1)P_(i)=1.

Therefore, in order to minimize (or reduce) the time domain channel meansquare error, an optimal

$F,{{- \frac{N}{4}} \leq F \leq \frac{N}{4}},{{and}\mspace{14mu} L},{1 \leq L \leq \frac{3N}{4}},$may be determined, so that equation (9) may be minimized.

The optimal uniform PDP, e.g., as discussed with respect to equations(13) to (18), may be based on PDP estimated from RS channelobservations. Because the sample duration in the PDP domain (asdiscussed with respect to equations (13) to (18)) is different from thesample duration of time domain signal for data REs, e.g.,

$\begin{matrix}{{{Sample}\mspace{14mu}{duration}\mspace{14mu}{of}\mspace{14mu}{RS}\mspace{14mu}{REs}^{\prime}\mspace{14mu}{PDP}} = {\frac{1}{{BW}_{RS}} = \frac{1}{N_{PDP} \times \Delta\; f \times \frac{12}{\rho}}}} & (19)\end{matrix}$In equation (19), ρ is the density of RS REs; and

$\begin{matrix}{{{Sample}\mspace{14mu}{duration}\mspace{14mu}{of}\mspace{14mu}{data}\mspace{14mu}{REs}^{\prime}\mspace{14mu}{PDP}} = {\frac{1}{{BW}_{system}} = \frac{1}{N_{FFT} \times \Delta\; f}}} & (20)\end{matrix}$

Therefore, in order to use the uniform PDP in FD-MMSE CE, the sampleduration of PDP may be converted into data RE channels' sample duration.

In some cases, a directly sample time conversion for estimated PDP maybe complicated. Since the aim of the embodiments of the example methodand system for DSE of the present disclosure is to find a uniform PDP toreplace the real PDP, an alternative way is to perform the sample timeconversion for the uniform PDP.

The uniform PDP used to calculate the frequency correlation after thesample time conversation may be assumed to have an FAP index F′ and alength L′, which may be represented as follows:F′=scaling factor×F,  (21)L′=scaling factor×L,  (22)

In equations (21) and (22), the scaling factor may be calculated as:

$\begin{matrix}{{{scaling}\mspace{14mu}{factor}} = {\frac{{Sample}\mspace{14mu}{duration}\mspace{14mu}{of}\mspace{14mu}{RS}\mspace{14mu}{PDP}}{{Sample}\mspace{14mu}{duration}\mspace{14mu}{of}\mspace{14mu}{data}\mspace{14mu}{REs}} = \frac{N_{IFFT} \times \Delta\; f}{N_{PDP} \times \Delta\; f \times \frac{12}{\rho}}}} & (23)\end{matrix}$

In equation (23), N_(IFFT) may be the size of Fast Fourier Transform(FFT) in the example system and N_(PDP) may be the length of theestimated PDP (e.g., input of the example method for DSE).

FIGS. 2A-2B illustrate examples of different sample time conversionschemes. For example, in one embodiment, as discussed above, a directlysample time conversion for estimated PDP may be complicated as shown inFIG. 2A. For example, 202 of FIG. 2A, may represent the PDP of RS, 204of FIG. 2A may represent the PDP of data, and 206 of FIG. 2A mayrepresent the uniform PDP for data CE. The PDP of data, as shown in 204of FIG. 2A, may be obtained by performing an interpolation 214 over thePDP of RS, as shown in 202 of FIG. 2A. Also, the uniform PDP for dataCE, as shown in 206 of FIG. 2A, may be obtained by obtaining a DSE 216of the PDP of data, as shown in 204 of FIG. 2A. According to one exampleembodiment, by utilizing the example method and system for DSE, auniform PDP may be determined to replace the real PDP, a sampleequivalent way may be to perform the sample time conversion for uniformPDP. For example, 208 of FIG. 2B, may represent the PDP of RS, 210 ofFIG. 2B may represent the uniform PDP for RS CE, and 212 of FIG. 2B mayrepresent the uniform PDP for data CE. The uniform PDP for RS CE, asshown in 210 of FIG. 2B, may be obtained by obtaining a DSE 218 of thePDP of RS, as shown in 208 of FIG. 2B. Also, the uniform PDP for dataCE, as shown in 212 of FIG. 2B, may be obtained by performing aninterpolation 220 over the uniform PDP for RS CE, as shown in 210 ofFIG. 2B.

The example method and system for DSE may obtain the optimal delayspread value to minimize the MSE of channel estimation (CE). The examplemethod and system for DSE may provide the optimal F and L that mayminimize or reduce the MSE between the estimated channel and the idealchannel using uniform PDP (as discussed with respect to equation (8)).Exhaustively searching F and L using the metric function in equation (8)may be one mechanism. However, such an approach may be computationallyexpensive because matrix inverse may be utilized for each hypothesis ofF and L. In order to reduce complexity, channel mean square error may becomputed by assuming a FD-MMSE CE is done using a uniform PDP.

With the above approximation, the optimization discussed with respect toequation (8) may eventually become the optimization as shown in equation(9). As discussed with respect to equation (9), equation (10), andequation (9A), that the computation for each hypothesis of F and Lbecomes much less using the equations (9), (10), or (9A).

FIG. 3 illustrates a block diagram representation of an example system300 to implement the example method for DSE of the present disclosure.The example system 300 includes a DSE module 302, a CE module 304, asymbol detector module 306, and a decoder module 308. The system 300 maybe inside a user equipment (UE) (e.g., a smart phone, a tablet, and acomputer).

In one embodiment, the DSE module 302 may receive an estimated noisevariance α² and an estimated PDP (e.g., P_(i)) from a time domain RSchannel estimation and may use the example DSE method to calculate anFAP index F′ and a length L′ (e.g., delay spread) in time domain. Theoutput F′ and L′ from the DSE module 302 may be used to calculate CE(e.g., as discussed with respect to equations (6), (7), and (8)) in theCE module 304. For example, in one embodiment, the F′ and L′ mayautomatically determine an optimal uniform PDP used in the CE module 304to calculate correlation matrices in equation (7) (e.g., not onlybetween RS channels and data RE channels).

The output from the CE module 304 may be used in the symbol detectormodule 306 along with a received signal. The output from the symboldetector module 306 may be transferred to the decoder module 308.

FIG. 4 illustrates another block diagram representation of an examplesystem for DSE of the present disclosure. For example, FIG. 4illustrates a detailed block diagram of the DSE module 302 of FIG. 3.

In one embodiment, the determination module 402 may receive an estimatednoise variance σ² and an estimated PDP (e.g., P_(i)) from time domain RSchannel estimation. At FAP index F=0 (e.g., when a value ‘0’ is assignedto F), a length L (e.g., delay spread) may be determined using acalculation metric (e.g., equation (9) or (18)) that may minimize thetime domain MSE using estimated noise variance σ² and the estimateduniform PDP from the time domain RS channel estimation. The estimatednoise variance σ² may be capped at a desired maximum SNR or the DSE maystop at a desired power cap. For example, the maximum SNR may be limitedto 20 dB when estimating delay spread.

In one embodiment, in both directions

${F < {0\mspace{14mu}( {{e.g.},{{- \frac{N}{4}} \leq F < 0}} )\mspace{14mu}{and}\mspace{14mu} F} > {0\mspace{14mu}( {{e.g.},{0 < F \leq \frac{N}{4}}} )}},$the optimal value of L that minimizes MSE for each F may be determined,as shown with respect to the selection module 404 and the change module410.

In one embodiment, a search for the optimal value of F and the optimalvalue of L in each direction may be stopped if the minimized MSEincreases as modulus F increases for n (e.g., n=5) consecutive times, asshown with respect to the stopping module 406 and the change module 410.

In one embodiment, an optimal F and corresponding L may be determinedbased on comparing all the minimized MSEs (e.g., output from thestopping module 406).

In one embodiment, the determined optimal value of F and the optimalvalue of L may be scaled based on the difference of sampling timebetween the RS and the data REs (e.g., using equation (21) and (22)), asshown with respect to a conversion module 408. The output F′ and L′ fromthe conversion module 408 may be used to calculate the CE and thefrequency correlation, as discussed with respect to equations (6), (7),and (8).

FIGS. 5A-5B illustrate a flow chart illustrating the example method forDSE of the present disclosure. The method of FIGS. 5A-5B may beimplemented in the DSE module 302 of FIG. 3 or the method of FIGS. 5A-5Bmay be implemented in modules 402, 404, 406, and 410 of FIG. 4. Forexample, the method 500 of FIGS. 5A-5B may determine an optimal FAPindex F and an optimal L (e.g., delay spread) to minimize the timedomain mean square error of channel estimation (as shown in equation(18)). For example, FIGS. 5A-5B illustrate an overall flow chart of theexample method for DSE of the present disclosure combined with the SNRand power cap approaches.

At 501, an example DSE system of the present disclosure (e.g., the DSEmodule 302 of FIG. 3 or the determination module 402 of FIG. 4) mayreceive an estimated noise variance σ² and an estimated PDP (e.g.,P_(i)) from a time domain RS channel estimation.

At 502, the example DSE system of the present disclosure (e.g., the DSEmodule 302 of FIG. 3) may cap the estimated noise variance σ² at adesired maximum SNR, for example, 20 dB.

At 503, the example DSE system of the present disclosure (e.g., the DSEmodule 302 of FIG. 3) may assign a value “0” to the FAP index F, i.e.,F=0. At 503, the example DSE system of the present disclosure (e.g., theDSE module 302) may determine the minimum MSE to be equal to 1 and theminimum MSE for the previous F to be equal to 100 (F=0, cnt=0,MSE_(min)=1, MSE_(min_prev_F)=100).

At 504, for L=1, the example DSE system of the present disclosure (e.g.,the determination module 402 of FIG. 4 or DSE module 302 of FIG. 3) maydetermine minimum MSE for current F to be equal to 100 and optimal L forcurrent F to be equal to −1 (L=1, MSE_(min_cur_F)=100, L_(opt, F)=−1).

At 505, the example DSE system of the present disclosure (e.g., thedetermination module 402 of FIG. 4 or the DSE module 302 of FIG. 3) maydetermine the MSE using equation (18):

$\begin{matrix}{{MSE} = {1 + \frac{L\;\sigma^{2}}{( {1 + {L\;\sigma^{2}}} )^{2}} + {\lbrack {\frac{1}{( {1 + {L\;\sigma^{2}}} )^{2}} - \frac{2}{1 + {L\;\sigma^{2}}}} \rbrack{\sum\limits_{i = F}^{L + F - 1}\; P_{i}}}}} & (18)\end{matrix}$

At 506, the example DSE system of the present disclosure (e.g., thedetermination module 402 of FIG. 4 or the DSE module 302 of FIG. 3) maydetermine if the calculated MSE at 505 is less than MSE_(min_cur_F)(e.g., MSE_(min_cur_F)=100) from 504.

However, in one embodiment, in 506, MSE_(min_cur_F) may not be a fixedvalue (e.g., 100). For example, in one embodiment, each time when themethod 500 returns to 506 from 513 through 505, MSE_(min_cur_F) maychange in 512. Therefore, in one embodiment, when 506 is executed forthe first time, MSE_(min_cur_F) may have the value 100.

If at 506, it is determined that the calculated MSE at 505 is not lessthan MSE_(min_cur_F) (e.g., MSE_(min_cur_F)=100) from 504, at 507, theexample DSE system of the present disclosure (e.g., the selection module404 of FIG. 4 or the DSE module 302 of FIG. 3) may determine if a L(e.g., length of uniform PDP P_(i)) is equal to ¾N_(PDP), because tosatisfy the time domain MSE of channel estimation (as discussed withrespect to equation (18)) the condition

$1 \leq L \leq \frac{3N}{4}$needs to be satisfied.

If at 506, the example DSE system of the present disclosure (e.g., thedetermination module 402 of FIG. 4 or the DSE module 302 of FIG. 3)determine that the calculated MSE at 505 is less than MSE_(min_cur_F),at 512, the example DSE system of the present disclosure (e.g., thedetermination module 402 of FIG. 4 or DSE module 302 of FIG. 3) maydetermine that the MSE_(min_cur_F) is equal to MSE (determined from 505)and L_(opt, F)=L. From 512, the method proceeds to 507.

If at 507, the example DSE system of the present disclosure (e.g., theselection module 404 of FIG. 4 or the DSE module 302 of FIG. 3)determines that the L (e.g., length of uniform PDP P_(i)) is not equalto ¾N_(PDP), at 508, the example DSE system of the present disclosure(e.g., the stopping module 406 of FIG. 4 or DSE module 302 of FIG. 3)may determine if Σ_(i=F) ^(L+F-1)P_(i)≥Thr_pwr. Thr_pwr may be based onthe estimated noise variance. For example, if SNR≤10, Thr_pwr=1 (nopower cap). However, if SNR>10, Thr_pwr=1−σ²*N/2.

If at 508, it is determined that Σ_(i=F) ^(L+F-1)P_(i)≥Thr_pwr, at 509,the example DSE system of the present disclosure (e.g., the DSE module302 of FIG. 3) may determine if MSE_(min_cur_F)<MSE_(min).

However, if at 508, it is determined that Σ_(i=F) ^(L+F-1)P_(i)≯Thr_pwr,at 513, the example DSE system of the present disclosure (e.g., thedetermination module 402 of FIG. 4) may increase the value of L and themethod returns to 505.

If at 509, it is determined that MSE_(min_cur_F)<MSE_(min), at 510, theexample DSE system of the present disclosure (e.g., the DSE module 302of FIG. 3) may determine that the MSE_(min)=MSE_(min_cur_F) F_(opt)=F,and L_(opt)=L_(opt,F). The search for the optimal L (L_(opt)) value andoptimal F (F_(opt)) value may be stopped.

At 511, optimal L (L_(opt)) and optimal F (F_(opt)) values are returned.These values may be sent to an internal block (e.g., conversion module408 of FIG. 4) of the example DSE system of the present disclosure.

If at 509, it is determined that MSE_(min_cur_F) is not less thanMSE_(min), the method proceeds to 511.

On the other hand, if at 507, it is determined that the L (e.g., lengthof uniform PDP P_(i)) is equal to ¾N_(PDP), at 514, the example DSEsystem of the present disclosure (e.g., the selection module 404 of FIG.4) may determine if MSE_(min_cur_F)<MSE_(min). If so, at 515, theexample DSE system of the present disclosure (e.g., the selection module404 of FIG. 4) may determine that the MSE_(min)=MSE_(min_cur_F),F_(opt)=F, L_(opt)=L_(opt,F). From 515, the method proceeds to 516.

However, if at 514, it is determined that MSE_(min_cur_F is) not lessthan MSE_(min), at 521, the example DSE system of the present disclosure(e.g., the change module 410 of FIG. 4) may determine if theMSE_(min_cur_F)>MSE_(min_prev_F) (minimum MSE for the previous value ofF). If so, the example DSE system of the present disclosure (e.g., thechange module 410 of FIG. 4) may increase the count cnt at 522.Otherwise, from 521, the method proceeds to 516. From 522, the methodproceeds to 516.

At 516, the example DSE system of the present disclosure (e.g., theselection module 404 of FIG. 4) may determine that theMSE_(min_prev_F)=MSE_(min_cur_F).

At 517, the example DSE system of the present disclosure (e.g., thechange module 410 of FIG. 4) may determine if F>0. If so, at 518, theexample DSE system of the present disclosure (e.g., the change module410 of FIG. 4) may determine if the count cnt==5 or F If so, from 518the method proceeds to 519. At 519, the example DSE system of thepresent disclosure (e.g., the change module 410 of FIG. 4) may determinethe count cnt==0 and F=−1. Otherwise, from 518, the method proceeds to520, where the example DSE system of the present disclosure (e.g., thechange module 410 of FIG. 4) may increase the value of F.

If at 517, if it is determined that F is not greater than or equal to 0,the method proceeds to 523. At 523, the example DSE system of thepresent disclosure (e.g., the stopping module 406 of FIG. 4) maydetermine if the count cnt==5 or F=−¼N. If so, the method proceeds to511.

Otherwise, the method proceeds to 524, where the example DSE system ofthe present disclosure (e.g., the DSE module 302 of FIG. 3) may decreasethe value of F.

From 524, 519, and 520 the method proceeds to 504.

The output from the method of FIGS. 5A-5B are the optimal value of L(L_(opt)) and the optimal value of F (F_(opt)), which are sent to aninternal block of the example DSE system of the present disclosure(e.g., the conversion module 408 of FIG. 4). In the internal block ofthe example DSE system of the present disclosure (e.g., the conversionmodule 408), the optimal value of L (L opt) and the optimal value of F(F_(opt)) received from another internal block of the example DSE systemof the present disclosure (e.g., the stopping module 406 of FIG. 4) maybe scaled based on the difference of sampling time between RS and dataREs (e.g., using equation (21) and (22)). The output F′ and L′ fromexample DSE system of the present disclosure (e.g., the conversionmodule 408) may be used to calculate CE and frequency correlation, asdiscussed with respect to equations (6), (7), and (8), in the CE module304 of FIG. 3.

In example embodiments, the example method for DSE (as discussed withrespect to FIGS. 5A-5B) may introduce two parameters L and F. Becauseexhausted search on F and L may not efficient, the complexity of theexample method for DSE (as discussed with respect to FIGS. 5A-5B) may bereduced compared to the alternative methods, since in the example methodfor DSE (as discussed with respect to FIGS. 5A-5B), the optimal F may benear value 0.

The implementation details of the example method for DSE (as discussedwith respect to FIGS. 5A-5B) may be as follows.

The implementation of the example method for DSE (as discussed withrespect to FIGS. 5A-5B) may effectively and efficiently obtain theoptimal DSE value in low SNR regime. However, in high SNR regime, theobtained DSE may be longer than the last channel taps because weak“ghost” taps shown in PDP estimation (caused by PDP estimation error andnoise). Two heuristic patches are used in some embodiments of theexample method for DSE (as discussed with respect to FIGS. 5A-5B) toprevent or reduce the increase of the delay spread in such scenarios.

Because, this DSE extension may happen when SNR is high, the maximum SNRmay be limited to some threshold value, for example, 20 dB (e.g., in theexample method for DSE (as discussed with respect to FIGS. 5A-5B)) whenestimating delay spread.

In order to further improve the performance, a power cap approach may beused for the example method for DSE (as discussed with respect to FIGS.5A-5B). For example, when calculating equation (18), if for any L and F,Σ_(i=F) ^(L+F-1)P_(i)≥Thr_pwr, the example method for DSE (as discussedwith respect to FIGS. 5A-5B) may stop searching and return the optimal Land F value. Thr_pwr may be based on the estimated noise variance. Forexample, if SNR≤10, Thr_pwr=1 (No power cap). However, If SNR>10,Thr_pwr=1−σ²*N/2.

FIG. 6 illustrates the BLER performance in low SNR regime and FIG. 7illustrates the BLER performance in high SNR regime. For example, asevident from FIG. 6 and FIG. 7, the example method may provide similarperformance as the ideal case assuming ideal knowledge of delay spread.

Therefore, the example method for DSE (as discussed with respect toFIGS. 5A-5B) may measure the delay spread from the estimated PDP and thenoise variance estimated in wideband CE of TRS. Through a time domaininterpretation of the frequency correlation, the example method for DSE(as discussed with respect to FIGS. 5A-5B) may be able to provide anoptimal delay spread value that may reduce or minimize the mean squareerror if the uniform PDP is used for FD-MMSE channel estimation.

In one embodiment, in the example method for DSE (as discussed withrespect to FIGS. 5A-5B), the searching step size of F and L may belarger than 1. In such a case, the starting index of F may be non 0, andthe stopping criteria of F may be a value that is not 5.

Also, the example method for DSE (as discussed with respect to FIGS.5A-5B) may not only be applied to the uniform PDP, but also may beapplied widely to other types of PDP, for example, an uniform PDP withsparsity.

In case of uniform PDP with sparsity, it may be assumed that a uniformPDP with length N and sparse factor α. In one embodiment, a may be anypositive integer that satisfies

${\alpha( {L - 1} )} < {\frac{3N}{4}.}$So the none zero entries are from index F to F+α(L−1), i.e., a PDP withentries {P_(i)′}, ∀i∈{F, F+1, . . . , F+α(L−1)} where

$\begin{matrix}{P_{i}^{\prime} = \{ \begin{matrix}{{1\text{/}L},} & {{i = {F + {\alpha\; k}}},{0 \leq k \leq {L - 1}}} \\{\mspace{20mu}{0,}} & {{otherwise}\mspace{166mu}}\end{matrix} } & (26)\end{matrix}$

In equation (26), k, F and L are integers

${F \in \{ {{- \frac{N}{4}},\ldots\;,\frac{N}{4}} \}},{{\alpha\; L} \in {\{ {1,\ldots\;,\frac{3N}{4}} \}.}}$The uniform PDP as discussed earlier in this paper may be a special casefor sparse uniform PDP when α=1.

In one embodiment, the time domain MMSE weights as discussed withrespect to the equation (12) for this sparse uniform PDP may berepresented as:

$\begin{matrix}{U_{i}^{\prime} = \{ \begin{matrix}{{\frac{1}{L}\text{/}( {\frac{1}{L} + \sigma^{2}} )},} & {{i = {F + {\alpha\; k}}},{0 \leq k \leq {L - 1}}} \\{\mspace{121mu}{0,}} & {{otherwise}\mspace{166mu}}\end{matrix} } & (27)\end{matrix}$

By using (27) in to (15), the optimal sparse uniform PDP may be obtainedfrom the following optimization:

$\begin{matrix}{{{\underset{F,L,\alpha}{argmin}\mspace{14mu} 1} + \frac{L\;\sigma^{2}}{( {1 + {L\;\sigma^{2}}} )^{2}} + {\lbrack {\frac{1}{( {1 + {L\;\sigma^{2}}} )^{2}} - \frac{2}{1 + {L\;\sigma^{2}}}} \rbrack{\sum\limits_{k = 0}^{L - 1}\; P_{F + {\alpha\; k}}}}}{{{s.t.1} \leq {\alpha\; L} \leq \frac{3N}{4}},{{- \frac{N}{4}} \leq F \leq {\frac{N}{4}.}}}} & (28)\end{matrix}$

In this example case, the optimal delay spread value is L′=αL+1. Thesparse uniform PDP may need a sample time conversion. When α>1, thereare multiple ways to do the interpolation. For example, similar toequations (21)-(22), in this case L″=scaling factor×L′, where thescaling factor can be calculated by equation (23).

The only difference between (18) and (28) is the accumulated sumcalculation. So it can be implemented in a same way as discussed abovewith respect to equation (18) with an additional searching layer for α.The implementation details can be summarized into following steps. Forexample, starting with α=1; assuming F=0, using (28) with estimatednoise variance σ² to find L to minimize MSE(F=0). Starting from twodirections, i.e., F<0 and F>0, for each F, find the optimal L and MSE.Searching on each direction may stop only if the minimized MSE keepincreasing as |F| increasing for consecutively five times. After bothdirection finish searching, for current α, all the MSE values may becompared to find an optimal F and its corresponding L. In oneembodiment, if α

${< \frac{3N}{8}},{\alpha = {\alpha + 1}}$and the method may start over assuming α=1. Further, the minimized MSEvalues may be compared corresponding to all the α, output the optimal αand its corresponding F and L.

It will be understood that, although the terms “first”, “second”,“third”, etc., may be used herein to describe various elements,components, regions, layers and/or sections, these elements, components,regions, layers and/or sections should not be limited by these terms.These terms are only used to distinguish one element, component, region,layer or section from another element, component, region, layer orsection. Thus, a first element, component, region, layer or sectiondiscussed herein could be termed a second element, component, region,layer or section, without departing from the scope of the presentdisclosure.

Spatially relative terms, such as “beneath”, “below”, “lower”, “under”,“above”, “upper” and the like, may be used herein for ease ofdescription to describe one element or feature's relationship to anotherelement(s) or feature(s) as illustrated in the figures. It will beunderstood that such spatially relative terms are intended to encompassdifferent orientations of the device in use or in operation, in additionto the orientation depicted in the figures. For example, if the devicein the figures is turned over, elements described as “below” or“beneath” or “under” other elements or features would then be oriented“above” the other elements or features. Thus, the example terms “below”and “under” can encompass both an orientation of above and below. Thedevice may be otherwise oriented (e.g., rotated 90 degrees or at otherorientations) and the spatially relative descriptors used herein shouldbe interpreted accordingly. In addition, it will also be understood thatwhen a layer is referred to as being “between” two layers, it can be theonly layer between the two layers, or one or more intervening layers mayalso be present.

The terminology used herein is for the purpose of describing particularembodiments only and is not intended to be limiting of the presentdisclosure. As used herein, the terms “substantially,” “about,” andsimilar terms are used as terms of approximation and not as terms ofdegree, and are intended to account for the inherent deviations inmeasured or calculated values that would be recognized by those ofordinary skill in the art.

As used herein, the singular forms “a” and “an” are intended to includethe plural forms as well, unless the context clearly indicatesotherwise. It will be further understood that the terms “comprises”and/or “comprising”, when used in this specification, specify thepresence of stated features, integers, steps, operations, elements,and/or components, but do not preclude the presence or addition of oneor more other features, integers, steps, operations, elements,components, and/or groups thereof. As used herein, the term “and/or”includes any and all combinations of one or more of the associatedlisted items. Expressions such as “at least one of,” when preceding alist of elements, modify the entire list of elements and do not modifythe individual elements of the list. Further, the use of “may” whendescribing embodiments of the present disclosure refers to “one or moreembodiments of the present disclosure”. Also, the term “exemplary” isintended to refer to an example or illustration. As used herein, theterms “use,” “using,” and “used” may be considered synonymous with theterms “utilize,” “utilizing,” and “utilized,” respectively.

It will be understood that when an element or layer is referred to asbeing “on”, “connected to”, “coupled to”, or “adjacent to” anotherelement or layer, it may be directly on, connected to, coupled to, oradjacent to the other element or layer, or one or more interveningelements or layers may be present. In contrast, when an element or layeris referred to as being “directly on”, “directly connected to”,“directly coupled to”, or “immediately adjacent to” another element orlayer, there are no intervening elements or layers present.

Any numerical range recited herein is intended to include all sub-rangesof the same numerical precision subsumed within the recited range. Forexample, a range of “1.0 to 10.0” is intended to include all subrangesbetween (and including) the recited minimum value of 1.0 and the recitedmaximum value of 10.0, that is, having a minimum value equal to orgreater than 1.0 and a maximum value equal to or less than 10.0, suchas, for example, 2.4 to 7.6. Any maximum numerical limitation recitedherein is intended to include all lower numerical limitations subsumedtherein and any minimum numerical limitation recited in thisspecification is intended to include all higher numerical limitationssubsumed therein.

In some embodiments, one or more outputs of the different embodiments ofthe methods and systems of the present disclosure may be transmitted toan electronics device coupled to or having a display device fordisplaying the one or more outputs or information regarding the one ormore outputs of the different embodiments of the methods and systems ofthe present disclosure.

The electronic or electric devices and/or any other relevant devices orcomponents according to embodiments of the present disclosure describedherein may be implemented utilizing any suitable hardware, firmware(e.g. an application-specific integrated circuit), software, or acombination of software, firmware, and hardware. For example, thevarious components of these devices may be formed on one integratedcircuit (IC) chip or on separate IC chips. Further, the variouscomponents of these devices may be implemented on a flexible printedcircuit film, a tape carrier package (TCP), a printed circuit board(PCB), or formed on one substrate. Further, the various components ofthese devices may be a process or thread, running on one or moreprocessors, in one or more computing devices, executing computer programinstructions and interacting with other system components for performingthe various functionalities described herein. The computer programinstructions are stored in a memory which may be implemented in acomputing device using a standard memory device, such as, for example, arandom access memory (RAM). The computer program instructions may alsobe stored in other non-transitory computer readable media such as, forexample, a CD-ROM, flash drive, or the like. Also, a person of skill inthe art should recognize that the functionality of various computingdevices may be combined or integrated into a single computing device, orthe functionality of a particular computing device may be distributedacross one or more other computing devices without departing from thespirit and scope of the exemplary embodiments of the present disclosure.

Although exemplary embodiments of system and method for providing firstarrival path (FAP) and delay spread estimation (DSE) in wirelesscommunication system have been specifically described and illustratedherein, many modifications and variations will be apparent to thoseskilled in the art. Accordingly, it is to be understood that a systemand method for providing first arrival path (FAP) and delay spreadestimation (DSE) in wireless communication system constructed accordingto principles of this disclosure may be embodied other than asspecifically described herein. The present disclosure is also defined inthe following claims, and equivalents thereof.

What is claimed is:
 1. A method for minimizing a time domain mean squareerror (MSE) of channel estimation (CE), the method comprising:estimating, by a processor, a power delay profile (PDP) from a timedomain observation of reference signal (RS) channels; estimating, by theprocessor, a noise variance of the RS channels; determining, by theprocessor, a first arrival path (FAP) value and a delay spreadestimation (DSE) value based on the estimated PDP and the estimatednoise variance; and determining, by the processor, a minimum value ofthe time domain MSE based on the estimated PDP, the estimated noisevariance, and a length of an uniform PDP.
 2. A method for minimizing atime domain mean square error (MSE) of channel estimation (CE), themethod comprising: estimating, by a processor, a power delay profile(PDP) from a time domain observation of reference signal (RS) channels;estimating, by the processor, a noise variance of the RS channels; anddetermining, by the processor, a first arrival path (FAP) value and adelay spread estimation (DSE) value based on the estimated PDP and theestimated noise variance for minimizing the MSE of CE, wherein the timedomain MSE is: $\begin{matrix}{{MSE} = {1 + \frac{L\sigma^{2}}{( {1 + {L\sigma^{2}}} )^{2}} + {\lbrack {\frac{1}{( {1 + {L\sigma^{2}}} )^{2}} - \frac{2}{1 + {L\sigma^{2}}}} \rbrack{\sum\limits_{i = F}^{L + F - 1}\; P_{i}}}}} & (1)\end{matrix}$ wherein F and L are integers, where:${1 \leq L \leq \frac{3N}{4}},{{- \frac{N}{4}} \leq F \leq {\frac{N}{4}.}}$wherein, σ² is the noise variance, P_(i) is power of an i-th channel tapor an uniform PDP, F is an index of the FAP, N is a length of theestimated PDP, and L is a length of the uniform PDP.
 3. The method ofclaim 2, wherein determining the FAP value and the DSE value to minimizethe time domain MSE comprises determining, by the processor, a value ofF and a value of L, wherein a minimum value of the time domain MSE isdetermined based on the value of F and the value of L.
 4. The method ofclaim 3, wherein the value of L is the delay spread value for minimizingthe MSE and the estimated noise variance is capped at a signal to noiseratio (SNR)=20 dB.
 5. The method of claim 3, wherein the determining thevalue of F and the value of L for minimizing the time domain MSEcomprises: assigning, by the processor, a value “0” to the index of theFAP F; determining, by the processor, a minimized value of MSE andcorresponding value of L for each F of a plurality of F values withinand${{- \frac{N}{4}} \leq F < {0\mspace{14mu}{and}\mspace{14mu} 0} < F \leq \frac{N}{4}};$determining, by the processor, the value of F and the value of L basedon comparing minimized values of MSE for the plurality of F valueswithin${- \frac{N}{4}} \leq F < {0\mspace{14mu}{and}\mspace{14mu} 0} < F \leq {\frac{N}{4}.}$6. The method of claim 5, wherein the value of F and the value of Lcorrespond to the minimum value of the time domain MSE from among theminimized values of MSE for the plurality of F values within${{- \frac{N}{4}} \leq F < {0\mspace{14mu}{and}\mspace{14mu} 0} < F \leq \frac{N}{4}},$wherein the minimized values of MSE and the corresponding values of Lare determined using equation (1).
 7. The method of claim 5, furthercomprising stopping a search of the value of F and the value of L forF >0 or F<0, by the processor, in response to the minimized value ofMSE, for F within${{- \frac{N}{4}} \leq F < {0\mspace{14mu}{or}\mspace{14mu} 0} < F \leq \frac{N}{4}},$being increased as |F| increased for n consecutive times, wherein the nis
 5. 8. The method of claim 5, further comprising scaling, by theprocessor, the value of F and the value of L based on a difference ofsampling time between the RS channels and data resource elements (REs)to determine a scaled value of F and a scaled value of L.
 9. The methodof claim 8, wherein the scaled value of F is F′, wherein F′=scalingfactor×F, and the scaled value of L is L′, wherein L′=scaling factor×L,wherein${{scaling}\mspace{14mu}{factor}} = {\frac{{Sample}\mspace{14mu}{duration}\mspace{14mu}{of}\mspace{14mu}{RS}\mspace{14mu}{PDP}}{{Sample}\mspace{14mu}{duration}\mspace{14mu}{of}\mspace{14mu}{data}\mspace{14mu}{REs}} = \frac{N_{IFFT} \times \Delta\; f}{N_{PDP} \times \Delta\; f \times \frac{12}{\rho}}}$wherein N_(IFFT) is a size of Fast Fourier Transform (FFT), N_(PDP) is alength of the estimated PDP, Δf is a subcarrier spacing, and p is adensity of RS REs.
 10. The method of claim 9, wherein the method furthercomprising: determining, by the processor, CE and a frequencycorrelation between the RS channels and the data REs, based on F′ andL′.
 11. A system for minimizing a time domain mean square error (MSE) ofchannel estimation (CE), the system comprising: a memory and a processorin communication with the memory, wherein the processor is configuredto: estimate a power delay profile (PDP) from time domain observation ofreference signal (RS) channels; estimate a noise variance of the RSchannels; determine a first arrival path (FAP) value and a delay spreadestimation (DSE) value based on the estimated PDP and the estimatednoise variance; and determine a minimum value of the time domain MSEbased on the estimated PDP, the estimated noise variance, and a lengthof an uniform PDP.
 12. The system of claim 11, wherein the time domainMSE is: $\begin{matrix}{{MSE} = {1 + \frac{L\sigma^{2}}{( {1 + {L\sigma^{2}}} )^{2}} + {\lbrack {\frac{1}{( {1 + {L\sigma^{2}}} )^{2}} - \frac{2}{1 + {L\sigma^{2}}}} \rbrack{\underset{i = F}{\sum\limits^{L + F - 1}}P_{i}}}}} & (1)\end{matrix}$ wherein F and L are integers, where:${1 \leq L \leq \frac{3N}{4}},{{- \frac{N}{4}} \leq F \leq {\frac{N}{4}.}}$wherein, σ² is the noise variance, P_(i) is power of an i-th channel tapor the uniform PDP, F is an index of the FAP, N is a length of theestimated PDP, and L is the length of the uniform PDP.
 13. The system ofclaim 12, wherein the processor is further configured to: determine theFAP value and the DSE value to minimize the time domain MSE based ondetermining a value of F and a value of L, wherein the processor isfurther configured to determine the minimum value of the time domain MSEbased on the value of F and the value of L.
 14. The system of claim 13,wherein the value of L is the delay spread value for minimizing the MSEand the estimated noise variance is capped at a signal to noise ratio(SNR)=20 dB.
 15. The system of claim 13, wherein the processor isfurther configured to: assign a value “0” to the index of the FAP F;determine a minimized value of MSE and corresponding value of L for eachF of a plurality of F values within arm${{- \frac{N}{4}} \leq F < {0\mspace{14mu}{and}\mspace{14mu} 0} < F \leq \frac{N}{4}};$determine the value of F and the value of L based on comparing minimizedvalues of MSE for the plurality of F values within${- \frac{N}{4}} \leq F < {0\mspace{14mu}{and}\mspace{14mu} 0} < F \leq {\frac{N}{4}.}$16. The system of claim 15, wherein the value of F and the value of Lcorrespond to the minimum value of the time domain MSE from among theminimized values of MSE for the plurality of F values within${{- \frac{N}{4}} \leq F < {0\mspace{14mu}{and}\mspace{14mu} 0} < F \leq \frac{N}{4}},$wherein the minimized values of MSE and the corresponding values of Lare determined using equation (1).
 17. The system of claim 15, whereinthe processor is further configured to stop a search of the value of Fand the value of L for F >0 or F<0, by the processor, in response to theminimized value of MSE, for F within${{- \frac{N}{4}} \leq F < {0\mspace{14mu}{and}\mspace{14mu} 0} < F \leq \frac{N}{4}},$being increased as |F| increased for n consecutive times, wherein the nis
 5. 18. The system of claim 15, wherein the processor is furtherconfigured to scale the value of F and the value of L based on adifference of sampling time between RS channels and data resourceelements (REs) to determine a scaled value of F and a scaled value of L.19. The system of claim 18, wherein the scaled value of F is F′, whereinF′=scaling factor×F, and the scaled value of L is L′, wherein L′=scalingfactor×L, wherein${{scaling}\mspace{14mu}{factor}} = {\frac{{Sample}\mspace{14mu}{duration}\mspace{14mu}{of}\mspace{14mu}{RS}\mspace{14mu}{PDP}}{{Sample}\mspace{14mu}{duration}\mspace{14mu}{of}\mspace{14mu}{data}\mspace{14mu}{REs}} = \frac{N_{IFFT} \times \Delta\; f}{N_{PDP} \times \Delta\; f \times \frac{12}{\rho}}}$wherein N_(IFFT) is a size of Fast Fourier Transform (FFT), N_(PDP) is alength of the estimated PDP, Δf is a subcarrier spacing, and p is adensity of RS REs.
 20. The system of claim 19, wherein the processor isfurther configured to determine CE and a frequency correlation betweenRS channels and data REs, based on F′ and L′.